CN104809480B - A kind of eye fundus image Segmentation Method of Retinal Blood Vessels based on post-class processing and AdaBoost - Google Patents

A kind of eye fundus image Segmentation Method of Retinal Blood Vessels based on post-class processing and AdaBoost Download PDF

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CN104809480B
CN104809480B CN201510262249.4A CN201510262249A CN104809480B CN 104809480 B CN104809480 B CN 104809480B CN 201510262249 A CN201510262249 A CN 201510262249A CN 104809480 B CN104809480 B CN 104809480B
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邹北骥
朱承璋
崔锦恺
向遥
李暄
张思剑
陈奇林
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Central South University
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    • G06F18/20—Analysing
    • G06F18/24—Classification techniques
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    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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    • G06T2207/30—Subject of image; Context of image processing
    • G06T2207/30004—Biomedical image processing
    • G06T2207/30041—Eye; Retina; Ophthalmic

Abstract

The invention discloses a kind of eye fundus image Segmentation Method of Retinal Blood Vessels based on post-class processing and AdaBoost, this method is 36 dimensional feature vectors including each pixel in the figure of eyeground constructs a divergence of a vector field feature including local feature, morphological feature and pixel, to judge whether it is pixel on blood vessel.During classified calculating, classified using post-class processing as Weak Classifier to sample set, then AdaBoost graders are trained to obtain strong classifier, and thus complete the classification judgement of each pixel, obtain segmentation result to the end.This method is preferable to vessel trunk extracting section, it is advantageous for the processing of high brightness focal zone, it is appropriate for post-processing, lesion for Major Vessels provides direct result, suitable for the area of computer aided quantitative analysis and medical diagnosis on disease of eye fundus image, there is apparent clinical meaning to the auxiliary diagnosis of relevant disease.

Description

It is a kind of to be divided based on the eye fundus image retinal vessel of post-class processing and AdaBoost Method
Technical field
The present invention relates to a kind of eye fundus image Segmentation Method of Retinal Blood Vessels, one kind is based on post-class processing and AdaBoost Eye fundus image Segmentation Method of Retinal Blood Vessels.
Background technology
Colored eyeground figure is to carry out the image that different angle shooting forms to eyeball inner wall using fundus camera.Eyeground figure Various Eye diseases, such as glaucoma, optic neuritis, maculopathy can be found as early as possible, it is convenient timely and effectively to treat.In addition, Retinal vessel is the blood vessel that noninvasive can be uniquely observed directly in Whole Body blood vessel, its shape, scale, is divided caliber Whether branch angle changes and whether has hyperplasia, exudation, the lesion of system vascular can be reacted, such as artery sclerosis, high blood The retinal microvascular of the patients such as pressure, diabetes, nephrosis has the performance of lesion.Therefore, eyeground figure can also be used as whole body The auxiliary diagnosis mode of health status, the Detection and Extraction of retina colour eyeground figure medium vessels, for associated various diseases Auxiliary diagnosis, auxiliary treatment and later observations all have important clinical medicine meaning.
Domestic and international many scholars are engaged in the work of this field, and achieve certain achievement.Retinal vessel segmentation at present Method is broadly divided into following several classes：Method based on pattern-recognition, the method based on matched filter, based on blood vessel tracing Method, the method based on mathematical morphology, multi-scale method, the method based on model.Wherein study more, segmentation effect is preferable Be method for classifying modes using supervised learning.For example, the green component of the extraction each pixel of RGB image such as Niemeijer Gray value, and the result that it is led by the use of Gauss matched filtering and Gauss single order second order is split as feature vector.Staal Deng a kind of blood vessel segmentation method based on crestal line of proposition.Two-Dimensional Gabor Wavelets and the gauss hybrid models grader such as Soares Blood vessel is split, the feature vector of each pixel is by the gray value and multiple dimensioned Two-Dimensional Gabor Wavelets transformation group Into.Ricci etc. carries out blood vessel segmentation with support vector machines.Osareh etc. is using multilayer neural network grader to eyeground figure blood Pipe point is classified, and starts to extract feature with principal component analysis.Lupascu etc. has studied AdaBoost graders, uses 41 feature vectors include unprecedented abundant vascular detail information.The supervised learning side based on Bagging such as Fraz Method obtains blood vessel classification results.It also all cannot be well to disease when matched filtering method or Mathematical Morphology Method is used alone Become eye fundus image and carry out blood vessel segmentation, be usually used in combination with other methods.Dividing method based on blood vessel tracing can be accurate Ground measures width and the direction of blood vessel, holds when but can only once track a blood vessel, and encounter vessel branch point or crosspoint Easily there is tracking mistake.In addition, the selection of initial seed point is also one of problem of blood vessel tracing method.Segmentation based on model Method is the method that uniquely can handle lesion eye fundus image well in all methods, can by the model for establishing different Blood vessel, background and lesion are distinguished, but there is also accuracy problems.
Due to being the application in medical industry, the accuracy and specificity of the blood vessel structure of extraction are realized to algorithm It is it is required that higher.Segmentation Method of Retinal Blood Vessels based on study is the highest method of accuracy rate in all methods, but existing Method to background, eye fundus image effect of the very non-uniform eye fundus image especially with lesion is bad, and accuracy rate is not It is high.
Invention content
For the deficiency of existing algorithm, the present invention proposes a kind of eye fundus image based on post-class processing and AdaBoost Segmentation Method of Retinal Blood Vessels, using AdaBoost adaptive iteration algorithms, vessel extraction precision is high.
A kind of eye fundus image Segmentation Method of Retinal Blood Vessels based on post-class processing and AdaBoost, including following step Suddenly：
Step 1：36 dimensional feature vectors are carried out to each pixel of the eye fundus image of known calibration result in training set Extraction；
36 dimensional feature vector includes 29 dimension local features, 6 dimension morphological features and 1 dimension divergence feature；
Wherein, the 29 dimension local feature includes 1 dimension grey value characteristics, 24 dimension Gaussian scale-space filtering characteristics, 4 successively Tie up Y-direction second order Gauss derivative feature；
The 1 dimension grey value characteristics are each gray value of the pixel on green channel in eye fundus image；
The 24 dimension Gaussian scale-space filtering characteristics are to carry out dimensional Gaussian filter in 4 different scales to eye fundus image The second order local derviation value of wave, the single order local derviation of 2-d gaussian filters and 2-d gaussian filters；
The 4 dimension Y-direction second order Gauss derivative is characterized in first obtaining the one-dimensional gaussian filtering of eye fundus image in the X direction X-direction one-dimensional filtering image, then the second order Gauss derivative of one-dimensional gaussian filtering image solution in the Y direction obtains to X-direction 4 A feature；
Wherein, the Gauss standard variance used in the one-dimensional gaussian filtering in the X-direction is 3；Two dimension in the Y-direction The value of Gauss standard variance used in gaussian filtering is followed successively by
The 6 dimension morphological feature is that 6 dimensional features that Bottom-Hat transformation obtains are carried out to eye fundus image；
The 1 dimension divergence is characterized in the summation Feature of the divergence of a vector field of all directions of different scale：
Wherein, (x, y) represents pixel point coordinates in eye fundus image, σ3For the filter scale of multi-scale filtering device, k is scale Parameter, σ3=k × 0.4；K=1,2......, 10；θ is direction vectorial in different scale, and λ is directioin parameter, θ=λ π/10； λ=1,2......10；It is the filtering figure for being filtered acquisition to eye fundus image using multi-scale filtering device Picture；
Step 2：Weak Classifier is generated using CART trees, the Weak Classifier based on generation obtains strong using AdaBoost algorithms Grader；
【Pixel in image is divided into two classes by the strong classifier, and one kind is blood vessel, and another kind of is background；
The CART trees are post-class processing；】
T iteration is carried out using AdaBoost algorithms, the eyeground of every width known calibration result in each iteration training set 36 dimensional feature vectors of each pixel of image are used as classification foundation, the manual markings classification results of combined training collection CART binary tree sorts, the node of the threshold value generation binary tree corresponding to the wrong feature vector for dividing rate minimum of selection, the two of construction Fork tree is as Weak Classifier；
The initial weight of the Weak Classifier obtained in first time iterative processT=1, m are training sample picture Vegetarian refreshments number, m values are 3 times of blood vessel pixel number, and it is 1 that positive negative sample, which chooses ratio,:2, positive sample, that is, puncta vasculosa, negative sample That is background dot；
The required mistake point rate used in each iterative processThe weak typing that an iteration obtains afterwards The weight D of devicet+1(i) with the weight D of preceding an iteration Weak Classifiert(i) relationship between is：
C represents weight parameter, the classification results H to be classified using Weak Classifier to pixelt(Zi) and the pixel Handmarking's result y of pointiWhen consistent, weight parameter C=0；Otherwise, C=1；yiValue be 1 or -1；
The depth of the CART trees is 2；
Step 3：It is treated using the T Weak Classifier linear combination that AdaBoost algorithms obtain into a strong classifier F (U) Test image is classified, and extracts the blood vessel structure in test image；
36 dimensional feature vectors that the pixel in segmentation image is extracted are treated in F (U) ∈ { -1,1 }, U expression.
【1 represents that segmentation result is puncta vasculosa, and -1 represents that segmentation result is background dot.】
Segmentation result that step 3 is obtained is carried out and is operated with mask, is obtained and operating result, pair in operating result figure Removal is less than the region of 20 pixels, obtains Optimized Segmentation result.
It is described to eye fundus image 4 different scales carry out 2-d gaussian filters, 2-d gaussian filters single order local derviation with And the second order local derviation value of 2-d gaussian filters, it obtains as follows respectively：
2-d gaussian filters are carried out in 4 different scales：
The single order local derviation of 2-d gaussian filters is carried out in 4 different scales：
The second order local derviation of 2-d gaussian filters is carried out in 4 different scales：
Wherein, σ is the Gauss standard variance used in 2-d gaussian filters, that is, the scale filtered, in Gaussian scale-space Filtering has 4 scales every time, and σ values are respectively
The Bottom-Hat transformation refers to carry out eye fundus image on n different directions the spy that cap transformation in bottom obtains Sign, is superimposed for the bottom cap transformation results of each different size of structural element in all directions, as a spy Sign；Wherein, n different directions angular range is between 0 ° -180 °, and the length value range of structural element is 3 in the transformation of bottom cap A pixel increases by 4 pixels every time to 23 pixels.
Advantageous effect
The present invention proposes a kind of eye fundus image Segmentation Method of Retinal Blood Vessels based on post-class processing and AdaBoost, This method is that each pixel in the figure of eyeground constructs a divergence of a vector field for including local feature, morphological feature and pixel 36 dimensional feature vectors including feature, to judge whether it is pixel on blood vessel.During classified calculating, made with post-class processing Classify for Weak Classifier to sample set, then AdaBoost graders are trained to obtain strong classifier, and thus complete each The classification judgement of a pixel.As a result remove mask and the region less than threshold value (20 pixels) by post-processing, obtain Last segmentation result.Based on international public database DRIVE's the experimental results showed that, the accuracy of the mean of this method reaches 0.9618, and susceptibility and specificity are superior to the existing method based on supervised learning, vessel trunk extracting section is preferable, right It is advantageous in the processing of high brightness focal zone, post-processing is appropriate for, the lesion for Major Vessels provides direct result, Suitable for the area of computer aided quantitative analysis and medical diagnosis on disease of eye fundus image, there is apparent clinical meaning to the auxiliary diagnosis of relevant disease Justice.
Description of the drawings
Fig. 1 is the flow chart of the present invention；
Fig. 2 is that the result of the application the method for the invention of embodiment 1 illustrates, wherein (a) is colored eyeground figure, (b) is hand Dynamic segmentation result, (c) are this paper segmentation results, (d) ROC curve；
Fig. 3 is that the result of the application the method for the invention of embodiment 2 illustrates, wherein (a) is colored eyeground figure, (b) is hand Dynamic segmentation result, (c) are this paper segmentation results, (d) ROC curve；
Fig. 4 is that the result of the application the method for the invention of embodiment 3 illustrates, wherein (a) is colored eyeground figure, (b) is hand Dynamic segmentation result, (c) are this paper segmentation results, (d) ROC curve.
Specific embodiment
Below in conjunction with drawings and examples, the present invention is further illustrated.
A kind of eye fundus image Segmentation Method of Retinal Blood Vessels based on post-class processing and AdaBoost, as shown in Figure 1, packet Include following steps：
Step 1：36 dimensional feature vectors are carried out to each pixel of the eye fundus image of known calibration result in training set Extraction；
36 dimensional feature vector includes 29 dimension local features, 6 dimension morphological features and 1 dimension divergence feature；
Wherein, the 29 dimension local feature includes 1 dimension grey value characteristics, 24 dimension Gaussian scale-space filtering characteristics, 4 successively Tie up Y-direction second order Gauss derivative feature；
The 1 dimension grey value characteristics are each gray value of the pixel on green channel in eye fundus image；
The 24 dimension Gaussian scale-space filtering characteristics are to carry out dimensional Gaussian filter in 4 different scales to eye fundus image The second order local derviation value of wave, the single order local derviation of 2-d gaussian filters and 2-d gaussian filters；
The 4 dimension Y-direction second order Gauss derivative is characterized in first obtaining the one-dimensional gaussian filtering of eye fundus image in the X direction X-direction one-dimensional filtering image, then the second order Gauss derivative of one-dimensional gaussian filtering image solution in the Y direction obtains to X-direction 4 A feature；
Wherein, the Gauss standard variance used in the one-dimensional gaussian filtering in the X-direction is 3；Two dimension in the Y-direction The value of Gauss standard variance used in gaussian filtering is followed successively by
The 6 dimension morphological feature is that 6 dimensional features that Bottom-Hat transformation obtains are carried out to eye fundus image；
The 1 dimension divergence is characterized in the summation Feature of the divergence of a vector field of all directions of different scale：
Wherein, (x, y) represents pixel point coordinates in eye fundus image, σ3For the filter scale of multi-scale filtering device, k is scale Parameter, σ3=k × 0.4；K=1,2......, 10；θ is direction vectorial in different scale, and λ is directioin parameter, θ=λ π/10； λ=1,2......10；It is the filtering figure for being filtered acquisition to eye fundus image using multi-scale filtering device Picture；
Step 2：Weak Classifier is generated using CART trees, the Weak Classifier based on generation obtains strong using AdaBoost algorithms Grader；
【Pixel in image is divided into two classes by the strong classifier, and one kind is blood vessel, and another kind of is background；】
T iteration is carried out using AdaBoost algorithms, the eyeground of every width known calibration result in each iteration training set 36 dimensional feature vectors of each pixel of image are used as classification foundation, the manual markings classification results of combined training collection CART binary tree sorts, the node of the threshold value generation binary tree corresponding to the wrong feature vector for dividing rate minimum of selection, the two of construction Fork tree is as Weak Classifier；
The initial weight of the Weak Classifier obtained in first time iterative processT=1, m are training sample picture Vegetarian refreshments number, m values are 3 times of blood vessel pixel number, and it is 1 that positive negative sample, which chooses ratio,:2, positive sample, that is, puncta vasculosa, negative sample That is background dot；
The required mistake point rate used in each iterative processThe weak typing that an iteration obtains afterwards The weight D of devicet+1(i) with the weight D of preceding an iteration Weak Classifiert(i) relationship between is：
C represents weight parameter, the classification results H to be classified using Weak Classifier to pixelt(Zi) and the pixel Handmarking's result y of pointiWhen consistent, weight parameter C=0；Otherwise, C=1；yiValue be 1 or -1；
The depth of the CART trees is 2；
Step 3：It is treated using the T Weak Classifier linear combination that AdaBoost algorithms obtain into a strong classifier F (U) Test image is classified, and extracts the blood vessel structure in test image；
36 dimensional feature vectors that the pixel in segmentation image is extracted are treated in F (U) ∈ { -1,1 }, U expression.
Embodiment 1：
Processing is split to figure a shown in Fig. 2 according to method described herein, obtained handmarking's result and segmentation As a result respectively as shown in figure b and figure c, obtained ROC curve is as shown in figure d；From Fig. 2 it may be seen that segmentation result and Context of methods ROC curve (area between curve and X-coordinate axle can evaluate the quality of partitioning algorithm, area it is more big more It is good), the area AZ=0.9838 between curve and x-axis, it is known that the dividing method of this paper is accurate believable, and accuracy reaches To 0.9658, susceptibility reach 0.8358 and specificity reach 0.9820, the dividing method for preferably demonstrating this paper is accurate It is believable.
Embodiment 2：
Processing is split to figure a shown in Fig. 3 according to method described herein, obtained handmarking's result and segmentation As a result respectively as shown in figure b and figure c, obtained ROC curve is as shown in figure d；From Fig. 3 it may be seen that segmentation result and Context of methods ROC curve (area between curve and X-coordinate axle can evaluate the quality of partitioning algorithm, area it is more big more It is good), the area AZ=0.9802 between curve and x-axis, it is known that the dividing method of this paper is accurate believable, and accuracy reaches To 0.9711, susceptibility reach 0.7578 and specificity reach 0.9914, the dividing method for preferably demonstrating this paper is accurate It is believable.
Embodiment 3：
Processing is split to figure a shown in Fig. 4 according to method described herein, obtained handmarking's result and segmentation As a result respectively as shown in figure b and figure c, obtained ROC curve is as shown in figure d；From Fig. 4 it may be seen that segmentation result and Context of methods ROC curve (area between curve and X-coordinate axle can evaluate the quality of partitioning algorithm, area it is more big more It is good), the area AZ=0.9514 between curve and x-axis, it is known that the dividing method of this paper is accurate believable, and accuracy reaches To 0.9658, susceptibility reach 0.7011 and specificity reach 0.9747, the dividing method for preferably demonstrating this paper is accurate It is believable.
By the data of Fig. 2-Fig. 4 it is found that the area between ROC curve and x-axis is all more than 0.9500, accuracy exists More than 0.9500, specificity is more than 0.9700, and for susceptibility more than 0.7000, all indexs have very high level, it is known that The dividing method of this paper is accurate believable.
Az represents the area between curve and x coordinate axis in Fig. 2-Fig. 4, can evaluate the quality of partitioning algorithm, and area is got over Big better, abscissa false positive fraction represent false positive rate (false hits rate), ordinate true Positive fraction represent true positive rate (hit rate) accuracy Accuracy, susceptibility Sensitivity, specificity Specificity。
With accuracy (accuracy, Acc), susceptibility (sensitivity, Sn), specificity (specificity, SP) this Three indexs weigh the quality of segmentation result.Accuracy is exactly all correct pixels of division, and susceptibility is exactly correct draws The percentage of the puncta vasculosa divided, specificity is exactly the percentage of the background dot correctly divided.With following four variable come computational Can index, point to puncta vasculosa (true positive, TP), point to background dot (true negative, TN), the blood of misclassification Pipe point (false positive, FP), the background dot (false negative, FN) of misclassification.Each performance Index Calculation expression formula For
ROC curve can describe the quality of algorithm, and abscissa false positive fraction represent false positive rate Ordinate true positive fraction represent true positive rate
The test set picture of DRIVE databases is tested using context of methods, according to above-mentioned performance test Index is weighed, and 20 width eyeground figures all in test set are split, and experimental data gives every pictures referring to table 1 in table 1 Sliced time, accuracy (Acc), susceptibility (Sn), specificity (Sp) it can be seen that sliced time of context of methods from average value It is shorter, susceptibility, specific all higher, the excellent properties of context of methods
Table 2 gives context of methods compared with the performance of all kinds of eyeground figure blood vessel segmentation methods based on study, can see Go out herein that the accuracy that the method that is carried is obtained is higher, and property indices are also superior to other methods.
1 segmentation result performance indicator of the present invention of table
2 present invention of table is compared with other supervised learning methods and results

Claims (3)

  1. A kind of 1. eye fundus image Segmentation Method of Retinal Blood Vessels based on post-class processing and AdaBoost, which is characterized in that packet Include following steps：
    Step 1：The extraction of 36 dimensional feature vectors is carried out to each pixel of the eye fundus image of known calibration result in training set；
    36 dimensional feature vector includes 29 dimension local features, 6 dimension morphological features and 1 dimension divergence feature；
    Wherein, the 29 dimension local feature includes 1 dimension grey value characteristics, 24 dimension Gaussian scale-space filtering characteristics, 4 dimension Y successively Direction second order Gauss derivative feature；
    The 1 dimension grey value characteristics are each gray value of the pixel on green channel in eye fundus image；
    The 24 dimension Gaussian scale-space filtering characteristics are to carry out 2-d gaussian filters, two in 4 different scales to eye fundus image Tie up the single order local derviation of gaussian filtering and the second order local derviation value of 2-d gaussian filters；
    The 4 dimension Y-direction second order Gauss derivative is characterized in first obtaining X side to the one-dimensional gaussian filtering of eye fundus image in the X direction To one-dimensional filtering image, then 4 that the second order Gauss derivative that one-dimensional gaussian filtering image solves in the Y direction to X-direction obtains Feature；
    Wherein, the Gauss standard variance used in the one-dimensional gaussian filtering in the X-direction is 3；Dimensional Gaussian in the Y-direction The value of filtering Gauss standard variance used is followed successively by
    The 6 dimension morphological feature is that 6 dimensional features that Bottom-Hat transformation obtains are carried out to eye fundus image；
    The 1 dimension divergence is characterized in the summation Feature of the divergence of a vector field of all directions of different scale：
    Wherein, (x, y) represents pixel point coordinates in eye fundus image, σ3For the filter scale of multi-scale filtering device, k is scale parameter, σ3=k × 0.4；K=1,2......, 10；θ is direction vectorial in different scale, and λ is directioin parameter, θ=λ π/10；λ=1, 2......10；It is the filtering image for being filtered acquisition to eye fundus image using multi-scale filtering device；
    Step 2：Weak Classifier is generated using CART trees, the Weak Classifier based on generation obtains strong classification using AdaBoost algorithms Device；
    T iteration is carried out using AdaBoost algorithms, the eye fundus image of every width known calibration result in each iteration training set Each pixel 36 dimensional feature vectors as classification foundation, the manual markings classification results of combined training collection, with CART bis- Tree classification is pitched, chooses the node of the threshold value generation binary tree corresponding to the wrong feature vector for dividing rate minimum, the binary tree of construction makees For Weak Classifier；
    The initial weight of the Weak Classifier obtained in first time iterative processT=1, m are training sample pixel Number, m values are 3 times of blood vessel pixel number, and it is 1 that positive negative sample, which chooses ratio,:2, positive sample, that is, puncta vasculosa, negative sample is carried on the back Sight spot；
    The required mistake point rate used in each iterative processThe Weak Classifier that an iteration obtains afterwards Weight Dt+1(i) with the weight D of preceding an iteration Weak Classifiert(i) relationship between is：
    C represents weight parameter, the classification results H to be classified using Weak Classifier to pixelt(Zi) and the pixel Handmarking's result yiWhen consistent, weight parameter C=0；Otherwise, C=1；yiValue be 1 or -1；
    Wherein, αtRepresent the Weak Classifier combination parameter that the t times iterative process obtains,yiRepresent i-th of sample The handmarking of pixel is as a result, HtRepresent the Weak Classifier that the t times iterative process obtains, QtRepresent normalization factor,ZiFor 36 dimensional feature vectors of i-th of training sample pixel, i=1 ..., m；
    The depth of the CART trees is 2；
    Step 3：Using the T Weak Classifier linear combination that AdaBoost algorithms obtain into a strong classifier F (U) to be tested Image is classified, and extracts the blood vessel structure in test image；
    36 dimensional feature vectors that the pixel in segmentation image is extracted are treated in F (U) ∈ { -1,1 }, U expression；
    Segmentation result that step 3 is obtained is carried out and is operated with mask, is obtained and operating result, pair with being removed in operating result figure Less than the region of 20 pixels, Optimized Segmentation result is obtained.
  2. It is 2. according to claim 1 a kind of based on the segmentation of the eye fundus image retinal vessel of post-class processing and AdaBoost Method, which is characterized in that it is described to eye fundus image 4 different scales carry out 2-d gaussian filters, 2-d gaussian filters one The second order local derviation value of rank local derviation and 2-d gaussian filters, obtains as follows respectively：
    2-d gaussian filters are carried out in 4 different scales：
    The single order local derviation of 2-d gaussian filters is carried out in 4 different scales：
    The second order local derviation of 2-d gaussian filters is carried out in 4 different scales：
    Wherein, σ is the Gauss standard variance used in 2-d gaussian filters, that is, the scale filtered is each in Gaussian scale-space Filtering has 4 scales, and σ values are respectively
  3. 3. according to a kind of eye fundus image retina based on post-class processing and AdaBoost of claim 1-2 any one of them Blood vessel segmentation method, which is characterized in that the Bottom-Hat transformation refers to carry out bottom to eye fundus image on n different directions The feature that cap transformation obtains, one is superimposed upon for the bottom cap transformation results of each different size of structural element in all directions It rises, as a feature；Wherein, n different directions angular range is between 0 ° -180 °, the length of structural element in the transformation of bottom cap Value range is spent for 3 pixels to 23 pixels, increases by 4 pixels every time.
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